Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	19^58458+18	74754	Lelio R Paula	01/2015
9752	12^69265-35	74750	Lelio R Paula	02/2015
9753	(2^248291+830)/2	74743	Stefano Morozzi	01/2020
9755	11^71771-48000	74742	Enzo Doria	12/2012
9754	(7*10^74741+197)/3	74742	Robert Price	07/2017
9756	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
9757	2^248252-110105	74732	Enzo Doria	04/2014
9758	(7*10^74729+71)/3	74730	Robert Price	03/2016
9759	3^156614-50	74724	Lelio R Paula	01/2015
9760	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
9761	(2^248193+870)/2	74714	Stefano Morozzi	01/2020
9762	(2^248167+1178)/2	74706	Stefano Morozzi	01/2020
9763	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
9764	(2^248145+3866)/2	74699	Stefano Morozzi	01/2020
9765	125^35622+124	74697	Norbert Schneider	02/2015
9766	(2^248114+994)/2	74690	Stefano Morozzi	01/2020
9767	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
9768	20780^3927+3927^20780	74685	Hans Havermann	12/2019
9769	(86*10^74676-41)/9	74677	Robert Price	11/2015
9770	(2^248065+3650)/2	74675	Stefano Morozzi	01/2020
9771	(p(15711)#-4)/2	74672	Robert Price	09/2017
9772	10^74670+31	74671	Robert Price	01/2011
9773	10^74670-122463	74670	Patrick De Geest	05/2013
9774	2^248036-69	74667	Lelio R Paula	03/2012
9775	11^71698-6000	74666	Enzo Doria	12/2012
9776	(2^248032+406)/2	74665	Stefano Morozzi	01/2020
9777	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
9778	14^65139-45	74658	Lelio R Paula	01/2015
9779	17967^14288+14288^17967	74653	Hans Havermann	11/2019
9780	6^95921-133	74642	Lelio R Paula	01/2015
9781	11^71675+78	74642	Lelio R Paula	02/2015
9782	17875^14986+14986^17875	74641	Hans Havermann	12/2019
9783	(2^247931+1458)/2	74635	Stefano Morozzi	01/2020
9784	(166*10^74624-7)/3	74626	Robert Price	11/2020
9785	18^59449-91	74625	Lelio R Paula	01/2015
9786	(12696^18181-1)/12695	74605	Serge Batalov	08/2020
9787	6^95864-16043	74597	Enzo Doria	02/2013
9788	5*7^88261+6	74590	Lelio R Paula	10/2014
9789	9*5^106710+4	74589	Lelio R Paula	10/2014
9790	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
9791	21157^3352+3352^21157	74585	Hans Havermann	12/2019
9792	(265*10^74579+17)/3	74581	Robert Price	05/2016
9793	17798^15489+15489^17798	74575	Hans Havermann	11/2019
9794	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
9795	5^106682-24	74568	Lelio R Paula	08/2014
9796	(2^247686+1450)/2	74561	Stefano Morozzi	01/2020
9797	474^27863+27863^474	74556	Norbert Schneider	01/2017
9798	(14*10^74540+79)/3	74541	Robert Price	11/2017
9799	(2^247582+1630)/2	74530	Stefano Morozzi	01/2020
9800	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
9801	(1705^23059-1)/1704	74518	Serge Batalov	08/2020
9802	3^156161+2660	74508	Lelio R Paula	01/2015
9804	2^247474-58695	74498	Lelio R Paula	05/2013
9803	(2^247476+886)/2	74498	Stefano Morozzi	01/2020
9805	11^71519-90	74480	Enzo Doria	07/2012
9806	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
9808	(2^247394-7)/3	74473	Lelio R Paula	06/2012
9807	18^59328+17	74473	Lelio R Paula	01/2015
9809	2^247379-181	74469	Lelio R Paula	03/2012
9810	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
9811	18860^8877+8877^18860	74465	Hans Havermann	12/2019
9812	17355^17564-17564^17355	74462	Norbert Schneider	11/2019
9813	2^247344+2047	74458	Lelio R Paula	05/2013
9814	2^247311-1017	74449	Lelio R Paula	05/2013
9815	(2^247288+1938)/2	74441	Stefano Morozzi	01/2020
9816	2^247280+7	74439	Lelio R Paula	03/2012
9817	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
9818	3^156004-62	74433	Lelio R Paula	01/2015
9819	21865^2536+2536^21865	74432	Hans Havermann	11/2019
9820	(2^247223+1050)/2	74422	Stefano Morozzi	01/2020
9821	36095!2-64	74416	Robert Price	06/2015
9822	67699!4+16	74409	Robert Price	09/2019
9823	2^247165-3	74405	M. Frind & P. Underwood	07/2002
9824	2^247150+32769	74400	Lelio R Paula	05/2013
9825	(2^247130+3858)/2	74394	Stefano Morozzi	01/2020
9826	(2^247055+2426)/2	74371	Stefano Morozzi	01/2020
9827	12^68911+73	74368	Lelio R Paula	01/2015
9828	2^246999+74903	74355	Enzo Doria	04/2016
9829	2^246989-110643	74352	Enzo Doria	05/2014
9830	10^74350+279439	74351	Patrick De Geest	07/2017
9833	(10^74350+11)/3	74350	Robert Price	11/2014
9831	10^74350-400000001	74350	Robert Price	07/2017
9832	10^74350-716241	74350	Patrick De Geest	07/2017
9834	67647!4-512	74346	Robert Price	11/2019
9835	10^74335+13659	74336	Patrick De Geest	05/2013
9836	10^74335-53	74335	Robert Price	05/2011
9837	23360^1521+1521^23360	74335	Hans Havermann	11/2019
9838	(2^246914+3418)/2	74329	Stefano Morozzi	01/2020
9839	2^246906-1215	74327	Lelio R Paula	05/2013
9840	(2^246879+1494)/2	74318	Stefano Morozzi	01/2020
9841	2^246848+111	74309	Lelio R Paula	03/2012
9842	(2^246842+2490)/2	74307	Stefano Morozzi	01/2020
9844	6^95490-18443	74306	Enzo Doria	03/2013
9843	(2^246840+2902)/2	74306	Stefano Morozzi	01/2020
9845	18^59188-2369	74298	Enzo Doria	03/2013
9846	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
9847	2^246744+40755	74278	Lelio R Paula	05/2013
9848	(29*10^74276+91)/3	74277	Robert Price	03/2016
9849	17222^17533-17533^17222	74272	Norbert Schneider	11/2019
9850	(2^246720+3606)/2	74270	Stefano Morozzi	01/2020
9851	6^95441+163	74268	Lelio R Paula	01/2015
9852	(40734^16111-1)/40733	74267	Anonymous	11/2020
9853	(14235^17881-1)/14234	74263	Serge Batalov	08/2020
9854	V(390863)	74258	Serge Batalov	03/2015
9855	10^74254+91	74255	Robert Price	03/2011
9857	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
9856	10^74254-130569	74254	Patrick De Geest	05/2013
9858	771^25718+25718^771	74250	Norbert Schneider	10/2016
9859	2^246618+427	74240	Henri Lifchitz	02/2005
9860	88*10^74234+3	74236	Robert Price	11/2016
9861	8*10^74234-49	74235	Robert Price	04/2016
9862	(19648^17291-1)/19647	74232	Serge Batalov	08/2020
9863	2^246578+12285	74228	Lelio R Paula	05/2013
9864	(3^155569-5)/2	74225	Lelio R Paula	06/2012
9865	13^66628+46	74220	Lelio R Paula	01/2015
9866	(2^246534+3034)/2	74214	Stefano Morozzi	01/2020
9867	(2^246486+798)/2	74200	Stefano Morozzi	01/2020
9868	2^246476-17295	74197	Lelio R Paula	05/2013
9869	(2^246465+446)/2	74194	Stefano Morozzi	01/2020
9870	(61*10^74189-1)/3	74191	Robert Price	11/2017
9871	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
9872	5*2^246413-3	74179	Lelio R Paula	05/2014
9873	2^246386-28635	74170	Lelio R Paula	05/2013
9874	(2^246371+3050)/2	74165	Stefano Morozzi	01/2020
9875	2^246334-111245	74154	Enzo Doria	05/2014
9876	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
9877	15^63045+82	74147	Lelio R Paula	01/2015
9878	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
9879	(199^32251-1)/198	74139	Serge Batalov	08/2020
9880	(2^246277+2114)/2	74137	Stefano Morozzi	01/2020
9881	2^246268-110507	74135	Enzo Doria	05/2014
9882	3^155328+2660	74111	Lelio R Paula	01/2015
9884	2^246148-2786249	74098	Enzo Doria	03/2016
9883	19740^5671+5671^19740	74098	Hans Havermann	01/2020
9885	(2^246135+3386)/2	74094	Stefano Morozzi	01/2020
9886	(16*10^74092-19)/3	74093	Robert Price	03/2016
9887	2^246115-110767	74088	Enzo Doria	05/2014
9888	7^87666-68	74087	Lelio R Paula	08/2014
9889	(2^246091+1938)/2	74081	Stefano Morozzi	01/2020
9890	10^74079+1145141919	74080	Marisa Kirisame	03/2015
9891	10^74079+6219	74080	Patrick De Geest	03/2016
9892	10^74079-282707	74079	Patrick De Geest	03/2016
9893	129^35098+2	74078	Lelio R Paula	05/2013
9894	22193^2176+2176^22193	74073	Hans Havermann	12/2019
9895	17703^15278+15278^17703	74071	Hans Havermann	12/2019
9896	2^246025-112123	74061	Enzo Doria	06/2014
9897	(67*10^74045+17)/3	74047	Robert Price	02/2017
9898	(2^245944+2202)/2	74037	Stefano Morozzi	01/2020
9899	(2^245885+1446)/2	74019	Stefano Morozzi	01/2020
9900	(13769^17881-1)/13768	74004	Serge Batalov	08/2020
9901	2^245823+66831	74001	Marek Hubal	02/2017
9902	5^105869+42	74000	Lelio R Paula	08/2014
9903	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
9904	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
9905	(3^155048-7)/262	73975	Lelio R Paula	06/2012
9906	9998*2^245696+3	73966	Donovan Johnson	10/2004
9907	13^66400-80	73966	Lelio R Paula	01/2015
9909	(2^245704+9)/25	73963	Lelio R Paula	07/2012
9910	11^71023-7170	73963	Enzo Doria	01/2013
9908	3*10^73962+13	73963	Robert Price	08/2017
9911	(64758^15373-1)/64757	73960	Anonymous	11/2020
9912	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
9913	2^245629-2797813	73942	Eric Chen	03/2016
9914	2^245557-153	73921	Lelio R Paula	03/2012
9915	(77*10^73917-59)/9	73918	Robert Price	11/2017
9916	15010^17699+17699^15010	73918	Norbert Schneider	11/2019
9917	(12975^17971-1)/12974	73913	Serge Batalov	08/2020
9918	2^245525+1869881	73911	Enzo Doria	06/2016
9919	2^245522+159	73910	Lelio R Paula	03/2012
9920	(2^245507+1986)/2	73905	Stefano Morozzi	01/2020
9921	(13*10^73891-43)/3	73892	Robert Price	08/2017
9922	19^57783-56	73891	Lelio R Paula	01/2015
9923	7*10^73888+79	73889	Robert Price	02/2017
9924	(2^245449+942)/2	73888	Stefano Morozzi	01/2020
9925	6^94948+174281	73884	Mike Oakes	02/2011
9926	(2^245431+3630)/2	73882	Stefano Morozzi	01/2020
9927	11^70939-4860	73876	Enzo Doria	01/2013
9928	18637^9196+9196^18637	73870	Hans Havermann	01/2020
9929	2^245372+54615	73865	Lelio R Paula	05/2013
9930	2^245362-143	73862	Lelio R Paula	03/2012
9931	7^87396+6^(87396-1)	73859	Robert Price	03/2016
9932	(22*10^73853-37)/3	73854	Robert Price	05/2017
9933	5*10^73851-69	73852	Robert Price	02/2021
9934	5^105646-14246	73844	Enzo Doria	02/2013
9936	2^245290-41	73840	Lelio R Paula	03/2012
9935	2^245290-94395	73840	Lelio R Paula	05/2013
9937	15770^17589+17589^15770	73836	Norbert Schneider	10/2019
9938	12352^18043+18043^12352	73828	Norbert Schneider	11/2019
9939	(2^245240+3598)/2	73825	Stefano Morozzi	01/2020
9940	(2^245242+498)/2	73825	Stefano Morozzi	01/2020
9941	8*5^105600-7	73813	Lelio R Paula	10/2014
9942	7*5^105573-4	73794	Lelio R Paula	10/2014
9943	(2^245112+1122)/2	73786	Stefano Morozzi	01/2020
9944	20151^4570+4570^20151	73751	Hans Havermann	12/2019
9945	(2^244968+1318)/2	73743	Stefano Morozzi	01/2020
9946	18^58742-4805	73738	Enzo Doria	03/2013
9947	(7*10^73729+23)/3	73730	Robert Price	06/2020
9948	13^66179+66	73720	Lelio R Paula	01/2015
9949	(2^244881+942)/2	73717	Stefano Morozzi	01/2020
9950	(2^244883+1946)/2	73717	Stefano Morozzi	01/2020
9951	(82*10^73714-1)/9	73715	Robert Price	12/2014
9952	(2^244862+3682)/2	73711	Stefano Morozzi	01/2020
9953	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
9954	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
9955	(13*10^73701+17)/3	73702	Robert Price	06/2015
9956	2339662057597*10^73677+9	73690	Robert Price	03/2021
9957	6*10^73686-29	73687	Robert Price	08/2020
9958	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
9959	21213^2974+2974^21213	73680	Hans Havermann	01/2020
9960	(3^154421-4)/23	73677	Lelio R Paula	06/2012
9961	14596^17691+17691^14596	73670	Norbert Schneider	11/2019
9962	8*7^87170+5	73669	Lelio R Paula	10/2014
9963	(29*10^73659-113)/3	73660	Robert Price	11/2017
9964	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
9965	(3883^20521-1)/3882	73650	Serge Batalov	08/2020
9966	(4*10^73647-19)/3	73648	Robert Price	06/2017
9967	2^244618-2297	73638	Yves Minet	10/2009
9968	3*5^105344+8	73633	Lelio R Paula	10/2014
9969	(2^244588+2562)/2	73629	Stefano Morozzi	01/2020
9970	5^105334-14096	73626	Enzo Doria	02/2013
9971	(2^244562+1534)/2	73621	Stefano Morozzi	01/2020
9972	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
9973	2^244465-110185	73592	Enzo Doria	05/2014
9974	(2^244465+2934)/2	73591	Stefano Morozzi	01/2020
9975	2^244443+40755	73585	Lelio R Paula	05/2013
9976	23155^1506+1506^23155	73583	Hans Havermann	12/2019
9977	10^73579+987654321	73580	Robert Price	12/2019
9978	10^73579+124173	73580	Patrick De Geest	02/2020
9979	10^73579-176379	73579	Patrick De Geest	02/2020
9980	2^244404+3841	73573	Yves Minet	03/2011
9981	19770^5263+5263^19770	73569	Hans Havermann	12/2019
9982	9*10^73565-41	73566	Robert Price	08/2020
9983	2^244372-110627	73564	Enzo Doria	05/2014
9984	19778^5241+5241^19778	73563	Hans Havermann	12/2019
9985	(2^244349+2186)/2	73557	Stefano Morozzi	01/2020
9986	(2^244309+3710)/2	73545	Stefano Morozzi	01/2020
9987	18428^9783+9783^18428	73537	Hans Havermann	01/2020
9988	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
9989	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
9990	18140^11301+11301^18140	73524	Hans Havermann	12/2019
9991	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
9992	(9699^18439-1)/9698	73508	Serge Batalov	08/2020
9993	(2^244152+2058)/2	73497	Stefano Morozzi	01/2020
9994	(2^244109+1422)/2	73484	Stefano Morozzi	01/2020
9995	17063^17362+17362^17063	73477	Norbert Schneider	04/2019
9996	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
9997	18^58521+65	73460	Lelio R Paula	01/2015
9998	13^65940+36	73454	Lelio R Paula	01/2015
9999	19065^7112+7112^19065	73439	Hans Havermann	12/2019
10000	(625^26267+1)/626	73437	Richard Fischer	12/2017

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Probable Primes Top 10000

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